Community Pictures and Higher Level Tasks

Community Pictures and Higher Level Tasks

Brody at Michigan State University

Higher Level Tasks:

1. There are 135 students that need to be housed in Emmons Hall. There are an even number of Freshman, Sophomores, and Juniors. There are four floors in the building and there are 20 rooms on each floor. There are allowed to be 2 people per room. The rooms need to be filled up from the 1^st floor going up. How many Freshmen, Sophomores, and Juniors are there? Would all the rooms be filled up evenly throughout the entire building or would there be left over spots? If so, how many and why?

2. At orientation, there are a group of 99 students. The program directors want to split up the freshman, sophomores, and juniors evenly at each table. There are an even amount of freshman, sophomore, and juniors. There are 20 tables total and there are six seats at each table. If you were to distribute the students from each class evenly at each table, how many tables and seats would be left over? How many students from each class would it take to fill the rest of the seats?

Michigan State University Library

Idea: -Finding area/perimeter of the water fountain

                                                          BP Gas Station on Michigan Ave.

                                                 Ideas: -Finding the amount of gas it takes in gallons to fill a car

                                                          -How much gas you can get with a certain amount of money

Community Pictures and High Level Tasks

 7-11  This is a store located in the heart of East Lansing that is a convenience store most people in the community have visited or visit regularly.  Ideas for tasks:

• Prices of the different items (addition, subtraction, multiplication)
• Size of slurpee cups
• Laying out the parking lot

 Buffalo Wild Wings  This is a restaurant in East Lansing that many people are familiar with and visit.  It is located on Grand River which is a very popular area to walk around and visit.  Ideas for tasks:

• Pricing- how many wings can you get with different price combinations (boneless or regular)?
• Time- how long they have to wait for a seat if there are x amount of tables
• Area- how many tables they can fit in the building

Parking Garage  Commonly known as the "hamster cage", this parking garage is right off of Albert Rd. in the heart of East Lansing.  Since Grand River area has a lot of shops in one area and there are not many parking lots to choose from, this is where most people park.

Higher Level Tasks:

1.  A car is parked for 9 hours in the parking garage in a permit spot.  These spots are free from 6pm to 3am Monday through Friday, but are not available for parking on Saturdays and Sundays.  If you park in one of these spots it is a $25 ticket for the first 6 hours and then another $10 ticket for each hour after.  Give 3 different days and times that a car would pay different amounts for their time in the lot.

2.  The builders of the parking garage want to be able to fit 600 cars in the garage at once.  The tower can only be 250 feet tall.  Show three different ways to accommodate this amount of cars using different levels throughout the structure.

Higher order Tasks

The Elevator yard requires 217,800 sq. ft to operate.  The elevator must be placed in an area where it is around a railway on both sides as well as near a large highway for semi-trucks coming in.  Circle an area that the Elevator be built in the picture below so that no houses are disturbed (represented with red dots) and the above requirements are met.  Then re draw that area  and write down all of the dimensions of the area that you are planning on using.

1in=1 mile (5280 ft)

The pile of corn holds 1, 000, 000 Bushels.  One load of corn from a semi-truck is nearly 900 bushels , one load of corn in a dump truck is 500 bushels.  Not all of the farmers in the area have a semi-truck, and not all have a dump-truck.  How many loads would fill the pile?  There should be both semi-trucks and dump trucks in your answer.   

 The Ethanol Plant - Source of Debate in Riga over where to put it and if it was worth it

 Historic Three bridges in Blissfield, located over the River Raisin

 Skate Park in Blissfield, Source of heated debate and large scale community project.

Assessment in Mathematics - Implementing Effective Assessment (Jamie Goetz)

In this weeks readings there was a discussion on the many different types of assessment as well as arguments for assessments that seem more effective for planning future instruction and determining what the children are able of doing.  Within these articles I was able to see that an effective mathematics assessment is different from just the normal cut and dry fill in the blank or circle the correct solution tests that I am familiar with.  Assessment for mathematics, like most other subjects, can be more effective when open ended and providing children with an opportunity to be metacognitive and explain their process and reasoning in the answer (Stylianou 2000).

      In the Stylianou reading there was a large emphasis on providing children with assessments that give them the opportunity to explain their reasoning, which can most effectively be achieved through giving children open ended tasks (Stylianou 2000).  This approach is found to be beneficial as it provides teachers with the opportunity to see specific strengths and weaknesses, as well as where within the procedure the children have a misconception.  Children also use multiple strategies to reach a solution therefore it would be beneficial also to see their reasoning to determine the strategy that they are using as well to learn how to teach to appeal to each child’s background knowledge. 

      A question that I have concerning the readings however is how you might effectively implement these practices with young children who are not yet fluent writers and struggle putting their ideas onto paper.  In giving young children assessments it can be challenging to find something that is time effective, which can be presented to the entire class at one time and where all children participate so that the teacher thoroughly understands the thought processes of all children. 

If I were to begin to create a performance assessment I would rely most often on developing activities that really showcase the children’s prior knowledge and strategy use.  This would be an activity where the children would reach a personal solution first and then come together in small groups to talk about their reasoning in obtaining their solutions.  In order to obtain information from all of the groups then it may be necessary to record the discussions that are taking place in each of these groups.  This would be a running record of the words that the children are saying and the things that those individual children are doing (NCTM Assessment).   Instead of writing transcripts of this event it may also be beneficial to write short anecdotal records of the children when discussing the lesson with them individually and then rotating which children the instructor works with every day, hitting all children at least once or twice in a week.  This could be a non paper/pencil assessment that could be used, based on performance within either lesson. 

My MT, instead of giving children paper and pencil tests, will individually work with the children and go through all of their skills at one time and work through the children until she is complete.  She also constantly is monitoring their work and everyday performance in the classroom, using observations to collect information.  The only downfall from this approach is that through individual, one-on-one assessments, this is so time consuming that she is only able to do this right before report cards.  Informal assessments are also useful, but it can be challenging to observe all of the children when they are working on the task all at the same time, and do not necessarily explicitly explain their thinking in completing the problem.           

Hannah Bush- Initial Post

I thought that the YouTube video on the area and perimeter lesson was very interesting. I believed that the main mathematical goal of the lesson was trying to correlate area and perimeter without being too obvious. The way that the problem was set up gave the students' a chance to figure out what area was and why area was NOT perimeter. I liked the way that one friend did area, but then the "friend" was wrong because he solved for perimeter and not area. It really gave the students a chance to really think about how area and perimeter are different from each other. Overall, I think the goal of the lesson was to get the students to understand how to demonstrate and prove area, while in the process realizing what perimeter was (and why it was different).

The debriefing video gave me a really good idea on how observers are supposed to take notes and share them with colleagues. It was similar to what I understood about my lesson study directions for observers because each person focused on a certain group of students. When each person focuses on different students, it makes it more organized and gives more varied results. The debriefing video was different from what I understood about my lesson study directions for debriefers because I wasn't sure how the debriefing actually went about. I thought of it more as an open discussion rather than each person going around and sharing their findings. I suppose that after each person shares their findings, there would be more extended discussion about what ideas were brought up.

After reading the Whitenack article, I found that it is very important for the senior leading the math lesson to really focus on student mathematical discussion and reasoning. As the article states, "the classroom teacher must continuously monitor the discussion while giving students opportunities to develop ways to reason with others" (Whitenack, 2002). The senior leader needs to push students to come up with ways to get to the answer and ways to prove that answer is correct both independently and with other students. The students should feel like they are not just trying to get to the answer, but explore different mathematical options. As the observers, I feel that we need to watch for ways that students got to their answers. We need to make note about different methods that they used and different ways they explored the problem.

I think the most challenging part about the lesson plan study is implementing the lesson in a way that students really "dig in" to the math and provide results that are worth observing. I think any observations that we get will be worthwhile, but it's really important to know what you want to get out of it. I think it's challenging to try to plan for certain results, but you never know how it's going to go. I guess the uncertainty is the most difficult part of a lesson study.

I think the most beneficial aspect of lesson study for my learning as professional development besides putting it on my resume is getting the chance to actually observe a lesson and get to participate in a discussion afterward. In general, I think that talking with colleagues and exchanging ideas is helpful, but actually getting to debrief about a lesson plan get be really beneficial. Beyond just discussing with colleagues, I believe that getting practice observing mathematical reasoning between students is really helpful. You can get in the mind set of how you should be observing students in a classroom and how to lead a thoughtful, beneficial lesson discussion for students.

Differentiation and Questioning - Morgan Pertler

I think these articles have been some of the most helpful readings so far this semester.  Due to my own personal experiences with using differentiated instruction in my student teaching for the preschool I know how valuable it is.  I work with a wide range of abilities, ethnicities, social classes, and levels of understanding in my classroom.
I have 4 children that are on case-load (meaning that they have special needs), I have 6 children that are enrolled through Head Start (which is a federally funded organization for free preschool for families who are below poverty line), I have 4 children whose families speak another language at home, and I have children who operate at a cognitive level of a 2.5 year old ranging to an 7 or 8 year old's cognitive level.  These are real-life examples of why it is important to consider differentiated instruction in your teaching and in your plans.

I have taken a few classes on working with diverse learners and so many of these articles are a bit of a review of content.  The Murrey (2008) article, however, was an interesting article because it did not just talk about the different linguistic needs to consider when teaching ELL's but it also gave strategies for how you can accommodate these particular needs.  For example, it talked about different principles, what they meant, and strategies for teaching ELL's this principle in an organized chart (p.148).   Specially Designed Academic Instruction in English (SDAIE) had a lot of good strategies, such as using manipulatives, visual tools, graphic organizers, and supporting "Realia"--activities that relate to real life.  The Weist (2008) article also used a lot of the same strategies for learners and also talked about using the constructivist approach which helps children build on experiences through dialogue with peers and teachers and reflecting on concepts (Weist, 2008).  The teacher Mrs. Higgins in this article helped students have this experiences by strategically grouping the students based on language abilities.  I also liked that she thought about pairing children within the groupwork so that no child feels isolated or not included.  I think this teacher was using a lot of teaching strategies that can be used effectively in all classrooms, not just classrooms with ELL's.

The article that I found to be the most useful was the Robert article discussing teaching math to at-risk students.  Being that the school I work in has a lot of at-risk students it was particularly beneficial to read about different strategies for "Mathematics for All" because these are ways to do a lot of open-ended problem solving and challenging students to do higher level thinking in mathematics regardless of their prior knowledge in math and/or risk factors.  I love that she pushed her students and was pleasantly surprised.  I think that often times we underestimate the capabilities of students who come from rough situations and this was a refreshing article to read.   By helping her students feel value in the work they were doing, she is also increasing motivation as well as content understanding.

The Wilkins (2006) article about challenging gifted students is something I have not ever had to think about until my student teaching.  In particular there are two girls in my class who are gifted and are not being challenged enough in the classroom.  Often times they will lose motivation or not try on activities because it is too easy for them, so coming up with extensions for every lesson is something I have had to learn to do.  I have had to ask myself, "How can I challenge these students to take this problem or lesson to the next level?"  I have often had to think of them in my mind as Kindergarteners or 1st graders rather than 4 or 5 year olds.  Since I have really learned to differentiate my instruction, I have seen their abilities increase significantly.  They are more excited to come to school, they are less bored, and they are showing an eager interest in learning which is something I have not seen from them until I began doing this.

Sometimes these things are overlooked, but it is important to look at the class as whole first and think about what the range of abilities are in your classroom, the type of learners you have, and then think about how you can accommodate and challenge students based on these needs.  Overall, these articles had one message that rang true in each--know your students and plan your activities and lesson so that no child is forgotten.  This is something that is very hard to do as a teacher and takes a lot of extra work,  but it is really important to remember in order to give students the best learning experiences possible.

Teaching Measurement, Our Weaknesses, and How to Enhance Our Skills through Integration

Teaching Measurement, Our Weaknesses, and How to Enhance Our Skills through Integration

            Measurement is one of the weakest areas in mathematics standardized testing in children in schools in the United States.  Beyond just being a source of weakness for Untied States children it is also the content area which has the biggest disparity between Caucasian students and children of minorities.  This is confirmed through the testing scores of NAEP and TIMISS.  Many teachers cite the two systems of measurement in the United States for being a source of this weakness, as our students are unfamiliar with the metric system; however the actual source of these weaknesses seems to be deeper than this (Thompson & Preston, 2004). 

            Integrative lessons can be meaningful and beneficial for all content areas and can deepen the lessons learned in all of the areas that are infused together as well as make a lesson more connective to everyday life.  Integrative lesson plans are one of the greatest tools that teachers can use to enhance the learning of students in many content areas instead of focusing on one single area.  As was discussed in the reading “Is Math Politically Neutral” it is important to integrate other subjects into math, even in small ways, so that the children can be gaining the most from every lesson. (Felton 2010)  In this article the discussion was based more on infusing social studies related content and current events with math by creating political and educational story problems.  This is one way in which social studies knowledge can also be built in a primarily math lesson where the content learned in a similar problem, without the integration would strictly be math.  Children are learning about more information in the same amount of time and therefore are building more knowledge with these deeper lessons. 

            With measurement it is simple and effective to integrate measurement with science related concepts, where children can use measurement to accurately collect data with different experiments (Thompson & Preston, 2004).  This also makes the learning of measurement more realistic, as children are using it in a way that applies to actual everyday life situations. 

            The benefits of creating an integrative curriculum cannot be overlooked, as children can gain so much more information, and connect this information to their lives more easily, from an integrative lesson plan than a lesson plan more focused on a singular content area.  By creating these lessons, teachers are building their students up for more success in life as children are more apt to learn effectively about living in the real world, when encountering more real world, everyday problems in an integrative manner in school.